(The "1st" string is the string closest to the ground, the "5th"
string is the one closest to the sky when holding the banjo
normally.)

If you don't have a piano handy, but you've got a guitar
that's tuned in the usual way, or you've got a
pitch pipe meant for tuning guitars, the 2nd, 3rd, and 4th
strings of the banjo are tuned the same as the 2nd, 3rd, and 4th
strings of the guitar.

Once the 4th string is tuned, the 3rd string is tuned to the
same pitch as the 4th string fretted at the 5th fret.

The 2nd string is tuned to the pitch of the 3rd string at
the 4th fret.

The 1st string is tuned to the pitch of the 2nd string at
the 3rd fret.

The 5th string is tuned to the pitch of the 1st string at
the 5th fret.

Some other common tunings:

C tuning: From low to high: C, G, B, D, G

C tuning is the same as G tuning, except the 4th
string is tuned down a whole step (two frets). So, the 3rd
string will sound the same pitch as the 4th string fretted at
the 7th fret.